Question

please explain steps!!

Convert the boy binary floating point numbers below to decimal notation forseti 8 bits: SEEEEEFF and the bias is 7, where S-sign, E-Exponent acts on bits) 10 pt. / 5 pts es convert from 8 bit floating point binary format convert to: decimal +/-n.nn DS EEE (FFC - 0100 1.100 = -1,5 426 6 14.05 Yoryal = 15 +0111 1140=125 10110100 00111110 me floating point

Answer 1

$\small \color{blue}Answer:\;\;$

1)
1 0110 100
sign bit is 1(-ve)
exp bits are 0110
   => 0110
   => 0x2^3+1x2^2+1x2^1+0x2^0
   => 0x8+1x4+1x2+0x1
   => 0+4+2+0
   => 6
in decimal it is 6
so, exponent/bias is 6-7 = -1
frac bits are 1

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1.1 * 2^-1
1.1 in decimal is 1.5
   => 1.1
   => 1x2^0+1x2^-1
   => 1x1+1x0.5
   => 1+0.5
   => 1.5
so, 1.5 * 2^-1 in decimal is 0.75
so, 10110100 in IEEE-754 single precision format is -0.75
Answer: -0.75

2)
0 0111 110
sign bit is 0(+ve)
exp bits are 0111
   => 0111
   => 0x2^3+1x2^2+1x2^1+1x2^0
   => 0x8+1x4+1x2+1x1
   => 0+4+2+1
   => 7
in decimal it is 7
so, exponent/bias is 7-7 = 0
frac bits are 11

IEEE-754 Decimal value is 1.frac * 2^exponent
IEEE-754 Decimal value is 1.11 * 2^0
1.11 in decimal is 1.75
   => 1.11
   => 1x2^0+1x2^-1+1x2^-2
   => 1x1+1x0.5+1x0.25
   => 1+0.5+0.25
   => 1.75
so, 1.75 * 2^0 in decimal is 1.75
so, 00111110 in IEEE-754 single precision format is 1.75
Answer: 1.75

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